Page 446 - Air and Gas Drilling Manual

9-50 Air and Gas Drilling Manual
V
578 ft/sec
.
a5
Using Equation 6-75, the Reynolds number of the aerated drilling fluid as it
exits this annulus section, N Ra5, is
78
0
(. ) ( .656 . 0 563 )
5
N Ra5
. 0 000259
N Ra5 2 083
,
The Reynolds number calculation above is greater than 2,000 and less than 4,000.
This indicates that the flow condition is transitional. Therefore, the empirical
Colebrook equation (i.e., Equation 6-77) is used to determine the approximate
Fanning friction factor for this annulus section.
Using Equation 8-2, the average absolute surface roughness of this annulus
section, e av5, is
(. (. 2 (. (. 2
001)
0 656)
0 00015)
0 563)
4 4
e av5
0 656)
0 563)
(. 2 (. 2
4 4
.
e 0 0058 ft
av5
Equation 6-77 must be solved by trial and error. A value for f a5 must be selected
that will satisfy the Colebrook equation. This value is
f a5 0 088
.
The Colebrook equation is
0 0058
.
.
.
1 0 656 0 563 251
.
2 log
.
,
.
0 088 37 . 2 083 0 088
The right and left sides of the above yield
.
.
336 336
Equation 6-74 for the fifth increment in the annulus can be solved for the
pressure at the bottom of the increment, P a5. This involves selecting this upper